Second kind integral equations of mixed Volterra-Fredholm type \[ u(x,t)=g(x,t)+\lambda \int^{t}_{0}\int^{b}_{a}K(x,t,\xi,\tau)u(\xi,\tau)d\xi d\tau \] and their nonlinear counterparts arise in various physical and biological problems. We study existence and uniqueness of a solution, continuous time collocation, time discretization and their global and discrete convergence properties.